A NEKHOROSHEV TYPE THEOREM FOR THE FRACTIONAL NONLINEAR SCHRÖDINGER EQUATION

Xue Yang; Jieyu Liu; Jing Zhang

doi:10.11948/20240555

2025 Volume 15 Issue 6

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Xue Yang, Jieyu Liu, Jing Zhang. A NEKHOROSHEV TYPE THEOREM FOR THE FRACTIONAL NONLINEAR SCHRÖDINGER EQUATION[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3317-3344. doi: 10.11948/20240555

Citation:

Xue Yang, Jieyu Liu, Jing Zhang. A NEKHOROSHEV TYPE THEOREM FOR THE FRACTIONAL NONLINEAR SCHRÖDINGER EQUATION[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3317-3344. doi: 10.11948/20240555

A NEKHOROSHEV TYPE THEOREM FOR THE FRACTIONAL NONLINEAR SCHRÖDINGER EQUATION

1.
School of Mathematical Sciences, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, 200241, China

Author Bio: Email: yangxue03170204@163.com(X. Yang); Email: jzhang@math.ecnu.edu.cn(J. Zhang)
Corresponding author: Email: 52215500034@stu.ecnu.edu.cn(J. Liu)
Fund Project: Funding was provided by National Natural Science Foundation of China (Grant No. 11871023 and No. 12171315). This paper is supported in part by Science and Technology Commission of Shanghai Municipality (No. 22DZ2229014)

Abstract

Abstract

We prove a Nekhoroshev type theorem for the fractional nonlinear Schrödinger equation under Dirichlet boundary conditions. More precisely, our findings show that the solutions with $ \varepsilon $-small initial data in the Gevrey space remain in their small magnitude over time intervals of order $ \varepsilon^{-\lvert \ln\varepsilon\rvert^{\gamma}} $ with $ 0 <\gamma<1/10 $. The result can be proved by using Birkhoff normal form method and the so-called tame property of the nonlinearity in Gevrey space.
- Hamiltonian PDEs /
- Nekhoroshev theorem /
- fractional nonlinear Schrödinger equation /
- Birkhoff normal form /
- tame property
MSC: 37J40, 37K55, 35B35, 35Q35

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References

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